| Helical gears are widely used in high-speed and heavy-duty transmissions due to their advantages such as smooth transmission,high contact ratio and high load-bearing capacity.With the increasingly strict requirements on the reliability of the transmission system,the meshing characteristics,transmission efficiency and fatigue life of helical gears have become main hot spots in gear research.Gears are normally working under the conditions like the long-term operation and high slip-to-roll ratio,thus the meshing tooth surface will generate high instantaneous temperature,which will cause an great reduction on the viscosity of the lubricant,and the film thickness will be significantly reduced,which will lead to poor lubrication and wear on the tooth surface.Gear wear will significantly reduce the operating efficiency of the transmission system and affect the vibration response.Most research regard the influence of gear wear as a reduction on gear mesh stiffness,however,the influence of the wear on gear dynamic are rarely studied in detail.Therefore,the reduction of gear mesh stiffness induced by gear wear is quite limited,and the changes on gear mesh position induced by wear are normally neglected by researchers.The gear wear will change the backlash,further cause the deterioration on gear mesh impact.Under the effect of wear and multiple clearances,the gear transmission system exhibits strong nonlinear characteristics.However,due to the limited understanding of tooth surface wear and lubrication mechanism,coupled with the time-varying meshing characteristics of helical gears,the studies on vibration characteristics of helical gears caused by wear and multiple clearances are relatively limited.In order to make up this gap,this paper fully considers the wear state of the tooth surface under the mixed lubrication condition and establishes a wear dynamic model that considers the bearing clearance,the backlash and gear mesh impact induced by wear.Thus,the vibration response of the gear was comprehensively analyzed to achieve condition monitoring and diagnosis of gear wear and clearance change.Firstly,this paper analyzes the time-varying meshing characteristics of the helical gear and proposes a calculation method for the time-varying dynamic excitation of the helical gear.Then,through the analysis of the gear lubrication state,a helical gear wear model under the mixed lubrication state was established,and the tooth surface wear distribution under different operating conditions was studied.The model fully considered the asperity contact under the mixed lubrication state,and the effects of the lubricant film and the temperature rise of the tooth surface on wear are fully studied.Moreover,according to the transmission characteristics of the helical gear and the change of the backlash caused by wear,a mesh impact model of helical gear was established.In addition,a ten-degree-of-freedom dynamic model of helical gear was proposed to study the gear dynamic which fully considered the change on gear mesh stiffness and impact position induced by the wear,bearing clearance and backlash.Through this dynamic model,a numerical simulation was carried out to investigate the gear dynamic under different bearing clearances and different wear severities respectively.At the same time,the bearing clearance tests,and the gear fatigue test were carried out to verify the reliability of the dynamic model.Finally,the time synchronous average analysis method was used to analyze the vibration and acoustic signals,which reveals the changes of gear dynamic characteristics.The numerical simulation results obtained by the helical gear wear model show that the gear wear mainly occurs at the tooth root.This is caused by the high slide-to-roll ratio at the tooth root and the high temperature rise of the tooth surface,then the lubrication state will be deteriorated and result in the wear.Compared with the traditional Archard wear model,the wear depth obtained by the wear model in the mixed lubrication state is significantly reduced,and the wear depth on the tooth surface is unevenly distributed as the load of the tooth surface changes.Through the analysis of the gear meshing position,it can be observed that the wear will lead to the reduction on the operating pressure angle,the increase in the gear backlash and the gear impact force,thereby aggravate the dynamic gear transmission error and increase the dynamic meshing force.The analysis also shows that the wear will cause increase in the gear mesh impact,thus lead to the increase in the amplitude of gear meshing frequency and its harmonics.Moreover,the impact force will generate the components of the half meshing frequency and some harmonics in the spectrum.This change can provide a reliable theoretical basis for the prediction of gear wear.The numerical simulation and the experimental study were carried out to study the dynamic characteristics of gears under different bearing clearances.The results show that the increase in bearing clearance will lead to the increase of the radial displacement of the gear,which will lead to the increase in the center distance and the operating pressure angle and reduction on gear mesh stiffness.Besides,it also increases the gear backlash,which will aggravate the gear mesh impact.The spectrum analysis of the gear vibration demonstrates that the increase of the bearing clearance causes the amplitudes of gear meshing frequency and its harmonics to increase gradually.This change can reflect the influence of the bearing clearance on gear dynamic.The experimental analysis shows that the large clearance will cause fluctuation in gear radial motion,then deteriorate the gear dynamic.However,the small clearance also will cause more friction in the bearing which will also deteriorate the gear dynamic.The gear dynamic induced by tooth wear was numerically studied.Firstly,the operating pressure angle,contact force and impact force were investigated under different wear severities.Then,the gear dynamic responses were analyzed through the proposed gear dynamic model.The results demonstrate that the wear cause increase in the gear mesh impact force,further leads to the increase in the amplitude of the gear mesh frequency and its harmonics.Besides,the gear run-to-fatigue test was conducted to study the influence,and the time synchronous average method was used to reduce the random noise in vibration and acoustic signals collected experimentally.The analysis of the vibration responses shows that due to the low speed and poor lubrication state in the low-speed stage,the gears are subjected to wear,which further causes increase in the amplitudes of the meshing frequency and its harmonics and corresponding sidebands.The feature demonstrates that the gear dynamic will gradually deteriorate with the increasing wear.The experimental results verified the reliability of the numerical study and also show that proper analysis and processing of vibration and acoustic signals can characterize the wear process of gears,and then achieve the purpose of early fault diagnosis and condition monitoring. |
